Method for optical modulation at periodic optical structure band edges

ABSTRACT

In the band edge region, transmission and reflection of an optical wave can be made very sensitive to the change in radiation wavelength, a change in the modulator material refractive index, and/or a change in the material absorption. Controlling these parameters with the increased level of sensitivity is provided by modulation using the band edge region. A preferred embodiment method of the invention uses a periodic optical structure (i.e., a grating) on top of an optical waveguide structure. The combination of the periodic structure and the optical waveguide is designed so that the reflection and/or transmission of the guided wave have broad pass bands with narrow transition bands. The optical structure is exposed to an incident laser radiation with wavelength in one of the transition bands. Modulation of the incident laser radiation is controlled by the change in refractive index or absorption in the optical guided wave structure produced by the modulation voltage. The incident radiation is in transition band, instead of the center portion of the pass band. A preferred method for designing a suitable periodic optical structure having broad pass bands with narrow transition bands uses a high coupling coefficient between the periodic structure and the optical waveguide mode. Increasing the product of the coupling coefficient and the length of the grating narrows the transition region band and increases sensitivity of the modulation.

RELATED APPLICATIONS AND PRIORITY CLAIM

This application is related to prior provisional application Serial No.60/235,584 filed Sep. 27, 2000. This application claims priority fromthat prior application under 35 U.S.C. §119.

FIELD OF THE INVENTION

The invention is in the optoelectronic field. The invention isapplicable to optical modulation systems, including, for example,optical switching for digital signaling and small signal modulation foranalog applications.

BACKGROUND OF THE INVENTION

Optical modulators are used in a variety of systems. Controlledmodulation of laser light is useful in analog systems to produce anoutput proportional to the input signal. Digital optical systems, suchas fiber optic communication systems, use optical modulators to signaldigital signals. In such case, a modulator is controlled to turn on andoff. Digital optical modulators as signaling devices may also form thebasis for optical memories and general computer devices. Possibilitiesfor optical modulators in both digital and analog systems are increasedwith increased efficiency as measured with respect to the drive voltagerequired to produce the desired optical modulation.

Conventional modulators follow similar radio frequency transmissiontheory of attaining the desired transmission or reflection over thewidth of the pass band, typically attempting to use the center portionof the pass band or bands of the modulator. Conventional modulation ofoptical waves utilizes the change of the refractive index and/or thechange of the absorption coefficient as a function of applied voltage tomodulate the intensity or phase of an optical wave. Example conventionaldevices operating in this manner over their pass bands are theMach-Zehnder modulator, the electro-optical phase modulator, thesemiconductor electro-refraction modulator, and the electro-absorptionmodulator. Any of these modulators would be rendered more useful by anincreased efficiency as a function of drive voltage.

SUMMARY OF THE INVENTION

The method of the invention uses the band edge of periodic structuresfor an efficient modulation method. In the band edge region,transmission and reflection of an optical wave can be made verysensitive to the change in radiation wavelength, a change in themodulator material refractive index, and/or a change in the materialabsorption. Controlling these parameters with the increased level ofsensitivity is provided by modulation using the band edge region.

A preferred embodiment method of the invention uses a periodic opticalstructure (i.e., a grating) on top of an optical waveguide structure.The combination of the periodic structure and the optical waveguide isdesigned so that the reflection and/or transmission of the guided wavehave broad pass bands with narrow transition bands. The opticalstructure is exposed to an incident laser radiation with a wavelength inone of the transition bands. Modulation of the incident laser radiationis controlled by the change in refractive index or absorption in theoptical guided wave structure produced by the modulation voltage. Theincident radiation is in the transition band, instead of the centerportion of the pass band.

A preferred method for designing a suitable periodic optical structurehaving broad pass bands with narrow transition bands uses a highcoupling coefficient between the periodic structure and the opticalwaveguide mode. The larger the product of the coupling coefficient andthe length of the grating, the narrower the transition region band, andthe more sensitive the modulation. The periodicity is chosen (byfabrication and by applying a bias voltage) so that the wavelength forBragg reflection of the periodic structure is offset from (i.e.,mismatched to) the incident laser wavelength so that the laserwavelength is at the center of one of the transition bands. A suitablemethod for designing the combined structure is to vary variousdimensions and materials, including grating, waveguide, and electrode,so that there is a large electro-optic change of index or absorption, astrong coupling coefficient and length product, a low insertion loss,and sufficiently fast speed of operation for the intended application.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1a (cross sectional view) and 1b (side view) illustrate a devicestructure, including a waveguide and grating, to which the presentinvention is applied;

FIG. 2 shows a preferred embodiment structure including twoelectro-absorption modulators connected in tandem;

FIGS. 3a (cross sectional view) and 3b (side view) show a preferredembodiment device including a one-dimensional grating coupled to anoptical channel waveguide;

FIG. 4 is a simulation result of structure shown in FIG. 3;

FIG. 5 shows a periodic grating on top of typical x-cut LiNbO₃ channelwaveguide with electrode configuration and Ti diffused channel;

FIG. 6 is a plot of effective index change as a function of theelectrical bias voltage for two different overlap integral values, Γ,for the modulator shown in FIG. 5;

FIG. 7 is a plot of coupling coefficient C₀ for the grating of FIG. 5that has photo resist spun or SiO₂ deposited on top of the LiNbO₃channel waveguide;

FIG. 8 is a plot of the simulated equivalent V_(π) for various LiNbO₃Band Edge modulators as a function of the grating and electrode lengthfor several coupling coefficients C=C₀ and waveguide propagation loss;

FIG. 9 is a plot of the comparison of equivalent V_(π) at various 3-dBRC bandwidth for various types of LiNbO₃ and polymer modulators.

DETAILED DESCRIPTION OF THE INVENTION

A region of the band edge (the region between the pass and stop band)including a preferably sharp transition region near the stop band edgeis used for modulation of an optical wave. In this band edge region,transmission and reflection of an optical wave can be made verysensitive to the change in incident radiation wavelength, a change inthe modulators material refractive index, and/or a change in thematerial absorption. Controlling these parameters with increased levelsof sensitivity is provided in the band edge region. A small appliedvoltage change; for example, can lead, to a low voltage change digitalswitch, or a significant modulation effect in an analog device.

The high dispersion of periodic structures in the edge region of theirpass and stop band is used in the invention to greatly enhance themodulation of the optical wave. In many applications, modulation iscreated by electro-optical changes in the material medium that includechanges in either the refractive index or the absorption coefficient, orboth, as a function of an applied voltage or electric field. In otherapplications, wavelength variation of the optical radiation is convertedto amplitude variation of the optical wave, and the conversion rate canbe controlled by the bias. The method of the invention may be applied toexisting designs of modulators made from LiNbO₃, semiconductor, polymerand other materials by adding a grating in accordance with the band edgeprinciples of the invention.

According to a preferred embodiment of invention shown in FIGS. 1a and1b, an optical modulator 10 with a periodic grating 12 on a conductivesubstrate 13 is used that has its band edge region matched to an opticalwavelength or wavelengths of interest. Either the transmission orreflection of an optical wave is controlled in the band edge region. Thecontrol is highly sensitive and responsive to small changes, i.e., smallchanges in the incident radiation wavelength, any electro-optical changeof material refractive index, or any electro-optical change of thematerial absorption. For example, in the case of a one-dimensionalgrating coupled to an electro-optical channel waveguide, the sensitivityis controlled by the properties of the waveguide 14 (including residualpropagation loss, the electro-optical change of the index or absorptionproduced by the voltage applied to electrodes 15, and the field patternof the optical mode) and the design of the grating (including thegrafting length, the grating periodicity, the dielectric constant of thegrooves and cladding 16, the height of the grooves, and the shape of thegrooves, and the overlap of the grating with the optical mode ofpropagation).

The insertion loss of the modulator is important to the overalltransmission efficiency of the signals. As the temperature changes, thegrating periodicity changes. The laser wavelength may also shift in timewithin its stability limit. The DC bias voltage may need to be adjustedcontinuously to assure that the laser wavelength is located at theappropriate position of the band edge. For analog modulationapplications, the incident laser wavelength should be biased at thecenter of the transition band. For digital modulation applications, thelaser wavelength should be located at the beginning edge of thetransition band for the zero signal. The switching voltage of thedigital system must be controlled accurately so that the modulator willbe at the end of the transition band for the one signal. The accuracy ofthe switching voltage control may be reduced when the grating isapodized to reduce the secondary loops in the transition region.Environmental factors should also be considered as such factors mayaffect the effectiveness of a modulator with an enhanced ultra-sharpband edge reflection or transmission region. In designing a particularphysical embodiment modulator to implement the method of the invention,such factors should be considered.

There is a trade-off between modulation efficiency and the electricalbandwidth (or switching speed) of the modulation. The electricalbandwidth (or the switching speed) will be limited by the capacitance ofthe device seen by the driving circuit. The capacitance is proportionalto the device length. At high frequencies, there may be an additionallimitation due to the transit time of the optical waves in the device.The transit time is also longer for longer L. On the other hand, thelarger the L, the larger the C₀L and the higher the modulationefficiency. In the design of a particular modulation device to implementthe present method, it is desirable to optimize the modulationefficiency based on the electrical bandwidth required for a specificapplication.

A particular beneficial use of the present method is for RF photoniclink applications. In analog RF photo links, there are two importantmeasures of performance. The first measure is the RF efficiency which isthe ratio of the output signal power to the input signal power. Thesecond measure is the Spurious Free Dynamic Range of the link. A largeSpurious Free Dynamic Range (SFDR) is a primary system requirement. Itis the range of the minimum input signal power when the signal is equalto the noise in the system to the maximum input signal power when thenonlinear distortion of the input signal becomes equal to the noise.When there are two or more signals at slightly different frequencies,the 3^(rd) order interference nonlinear distortion of the signalsbecomes the primary nonlinear distortion. SFDR will depend on thenonlinear distortion of the modulator. Thus, it is beneficial tolinearize the modulator. Preferred techniques to linearize themodulation include a two-wavelength design and a split electrode designfor the cancellation of the nth order nonlinearity. FIG. 2 shows aschematic diagram of the latter split electrode design, in which twomodulators 20 are connected in tandem. The particular modulators 20shown are electro-absorption modulators where an applied voltage toelectrodes 22, 24 is used to shift the absorption edge in the intrinsic(i) region. Different voltages are applied on the two electrodes 22, 24.By properly choosing the voltage and the electrode lengths, certainorders of non-linearity can cancel each other. Thus the SFDR of the RFoptical fiber link can be increased.

A preferred example that illustrates the principles of the presentmethod will now be discussed. This example, shown in FIGS. 3a and 3b, isa one-dimensional grating 26 coupled to an optical channel waveguide 27that has an efficient electro-optical change of index. In this example,the waveguide has no residual propagation loss. As before, materialproperties, including substrate 29, and voltage applied to electrodes 29affect performance. There can be various choice of materials for thechannel waveguide, different configurations for the grating grooves andmaterial and different configurations for the electrode.

The pass and stop bands of such a grating depend on the couplingcoefficient C₀ of the grating with respect to the optical guided wavemode. For grating corrugation with rectangular grooves, C₀ is givenapproximately by $\begin{matrix}{C_{0} \approx {\frac{\omega}{2}{\Delta ɛh}{\int_{0}^{w}\quad{{\mathbb{d}y}{{{e( {\frac{d}{2},y} )}}^{2}.}}}}} & (1)\end{matrix}$where ω represents the optical angular frequency; Δε is the change inthe dielectric constant in the grating corrugation; and h, W are thegrating corrugation height and width, respectively. h∫₀ ^(w) dy|e(d/2,y)|² represents the portion of the light intensity over the gratingarea. The larger the h, Δε and |e|², the larger the C₀. When a voltageis applied to the optical waveguide via the two electrodes 29, itcreates an electric field. There will be a change of the effective indexof the optical waveguide mode produced by the electric field.

FIG. 4 is a simulation result of the FIG. 3 structure. It shows thevariation of the reflectivity (and transmission) of the device atvarious δ_(k)L values for several coupling strength C₀L. δ_(k)L is 2πtimes the off-set of the number of half-wave number in the opticalwaveguide to the number of the grooves in the grating, as discussed inthe text. The δ_(k) is controlled by the grating periodicity Δ, theeffective index of the waveguide mode and the free space wavelength ofthe optical guided wave. The stop band is the broad high reflectivity(or low transmission) main lobe around δ_(k)L=0, and the pass band isthe low reflectivity (or high transmission) region at δ_(k)L>20. Theband edge is between the pass and the stop bands. There are twosecondary lobes shown in the transition region in this figure.

FIG. 4 shows the reflection and the transmission of the waveguide with agrating overlay of length L as a function of δ_(k), the mismatch fromthe Bragg condition. δ_(k) has two parts. There is a bias δ_(k0)(created by the effective index of the optical guided wave at free spacewavelength λ under the applied bias voltage in the absence of the signalvoltage) and a signal δ_(ks) (created by the modulation voltage).$\begin{matrix}{\delta_{k} = {\delta_{k0} + \delta_{ks}}} \\{{\delta_{k0} = {2{\pi( {\frac{2n_{{eff},{bias}}}{\lambda} - \frac{1}{\Lambda}} )}}},} \\{\delta_{ks} = \frac{4{\pi\Delta n}_{eff}}{\lambda}}\end{matrix}$where Λ is the grating periodicity, n_(eff,bias) is the effective indexof the guided wave with the bias voltage applied, and Δn_(eff) is thechange of effective index created by the modulation voltage. Theeffective index of the guided wave, n_(eff), is the sum of n_(eff,bias)and Δn_(eff). In other words, δ_(k)L is 2π times the off-set of thenumber of half-wave number in the optical waveguide, under the gratingat the applied voltage, to the number of the grooves in the grating. TheBragg reflection occurs at Δ=λ/2n_(eff), i.e. δ_(k)=0. As δ_(k) isshifted from the bias value by the change of effective index of theguided wave mode due to the electro-optical effect of the modulationvoltage, the reflection or the transmission of the optical intensitycoupled from the waveguide to the fibers is changed.

At large C₀L where L is the length of the grating, the width of the passband is broadened while the center of the stop band does not change. Theresult is a very rapid variation from pass to stop band (i.e., thetransition) as a function of both the wavelength and the effective indexof the waveguide. The larger the C₀L, the sharper is the transition.With the method of the invention using a large C₀L and a wavelength λand n_(eff,bias) such that δ_(k0) is within the band edge region at thesharp transition between pass and stop bands, a small change of theeffective index will now lead to a very large change of transmission orreflection from pass to stop band. In implementing the invention foranalog modulation, δ_(k0) is preferably biased to the value that yieldsthe largest slope, i.e. dR/dδ_(k) or dT/dδ_(k). For digital modulation,δ_(k0) is preferably biased to yield the highest on/off ratio with asmallest change of δ_(k) Because of the existence of the secondarylobes, the switching voltage needs to be controlled to yield a highon/off ratio. Secondary lobes of R or T can be suppressed by apodizationof grating periodicity.

In addition to the grating, the most effective design of the waveguideand the electrodes will cause a most effective change of the effectiveindex of the optical waveguide mode by the applied signal voltage, inconformity with obtaining a large C₀ and within the bandwidth allowed bythe capacitance and the transit time. The larger the Δn_(eff) for agiven modulation voltage, the larger the modulation efficiency. Thereare number of known optical waveguide materials and structures such asthe LiNbO₃ and polymer waveguides in addition to new waveguide materialsthat will be a good candidate for the channel waveguide. The electrodedesign should be configured and optimized separately for each case.

Though the one-dimensional grating and LiNbO₃ waveguide provides belowan important example of the use of the method of the invention, theinvention may be applied to any material, waveguide structure andelectrode design that has an electro-optical change of index. It canalso be applied to materials that have electro-absorption effects.Though the reflector modulator is used as an example to illustrate theband edge region modulation, transmission modulators may also be used inaccordance with the method of the invention. The performance oftransmission modulators will be similar to the reflection modulators.For reflection modulation, a circulator is required between the laserand the modulator. For transmission modulation, an isolator is requiredbetween the laser and the modulator.

For most optical waveguides, the electrical properties of the twoelectrodes can be represented as a capacitor associated with resistors.The actual voltage from the RF modulation source required to achieve agiven electric field depends on the circuit properties of the device andthe driving circuit. There will be a drop of the electric field at highfrequencies due to the RC effect in circuits. This is the primary causeof the bandwidth restriction. The other cause is the transit timerequired for the optical energy to decay to a low level. The transittime and the capacitance can be reduced by decreasing L. On the otherhand, there is a limit of how large a coupling coefficient C₀ betweenthe grating and the optical mode can be obtained. The smaller the C₀L,the less sensitive the modulation. Therefore, there will be a trade-offbetween V_(π) and the bandwidth.

The invention is generally practiced through matching the bias effectiveindex and the wavelength to the band edge region, and may be enhancedthrough optimizing the shape of the band edge region of the modulator.Five major design considerations may be applied to perfect anoptimization for a given practical embodiment and set of wavelengths ofinterest:

-   -   (1) The larger the C₀L product, the more sensitive the        modulation. On the other hand, the smaller the L, the larger the        bandwidth. Thus, one of the important design considerations of        such a modulator is to design the waveguide and the grating to        obtain as large a C₀ as possible. For polymer and LiNbO₃        waveguides, various known material parameters and fabrication        techniques can be used to obtain a large C₀.    -   (2) Obtaining as large a Δn_(eff) as possible for a given        voltage. Again, for the LiNbO₃ and polymer waveguides, the δ_(k)        as a function of applied voltage can be obtained based on the        known electro-optical coefficients and the electrode and        waveguide designs.    -   (3) In a more detailed analysis of R or T, the sharpness of the        transition region is reduced significantly by higher propagation        loss. The slope, dR/dδ_(k) or dT/dδ_(k), is reduced as the        propagation loss increases. Therefore, the third major design        consideration is to reduce the propagation loss and to achieve        the best performance for a given propagation loss. The        realization and the assessment of the effect of propagation loss        will guide the development of material and fabrication        technology for manufacturing. We also discovered that for a        given effective absorption coefficient, α_(eff), there is an        optimum L_(opt) that yields the largest slope. However, whether        the optimum L_(opt) should be used for a given application        depends on other design considerations such as the bandwidth to        be discussed in (4)    -   (4) The voltage will be applied to the modulator electrode        across the grating via the RF and microwave circuit. For the        modulator designed as a lumped circuit element, it is basically        a capacitance C in the electrical circuit. There will be a drop        of the voltage applied to the modulator at higher frequencies        due to the circuit property, called the RC effect. The frequency        range from DC to the frequency at which the modulator voltage is        dropped to 1/√{square root over (2)} of its peak value at DC is        called the broadband bandwidth of the modulator. The larger the        C, the smaller the bandwidth. On the other hand, C is        proportional to the length of the electrode that equals to the        length of the grating L. Therefore, the larger the bandwidth        required for a specific application, the shorter must be the L.        L affects the modulation slope, dR/dδ_(k) or dT/dδ_(k), or the        “on/off δ_(k)” because it affects the C₀L, α_(eff)L and δ_(k)L        values. For this reason, the fourth major design consideration        is to optimize the design based on the required L.    -   (5) For external modulators inserted into optical fiber links,        the insertion loss of the modulator is the fifth major design        consideration. For analog links, the RF link efficiency is        proportional to the product of modulation slope efficiency and        the insertion efficiency at the bias voltage. For digital links,        the insertion efficiency at the “on” state of the modulator        determines the optical power that can be distributed and        transmitted. The on/off ratio determines the signal to noise        ratio at the receiver. The insertion efficiency t_(m) will        depend on the modulator (including the grating) design as well        as external factors such as the insertion loss of the circulator        used for reflection modulators, the coupling loss to the fibers,        etc.

For illustration purposes, the invention has been illustrated primarilyin terms of the electrode designed as a lumped electrical circuitelement. There are other electrical designs that will avoid the RCbandwidth limit. For example, an impedance matching circuit may beemployed to give high modulation efficiency over a narrow band offrequency around a high center frequency using a modulator with a largerL. The traveling wave electrode design is the traditional way toincrease the bandwidth without requiring a shorter L at highfrequencies. However, the traveling wave electrode will not work wellfor a resonant modulator based on the interaction of forward andbackward propagating waves. In addition to the RC limitation inbandwidth, there is a transit time limitation to the bandwidth of amodulator. For a grating modulator, it takes a finite amount of time(i.e. the transit time) for the interaction between forward and backwardpropagating wave to reach equilibrium or to decay.

Modulation of R or T is also obtained when the absorption coefficient αis changed by the applied voltage. In semiconductors, a large change ofabsorption coefficient, called the electro-absorption effect, can beobtained in material structures such as the multiple quantum wellstructures. Simultaneously, there will be change of index of refractiveindex called the electro-refraction. Electro-absorption andelectro-refraction effects occur simultaneously. However, materialsstructures can be designed to optimize electro-absorption or to optimizeelectro-refraction. The optimization of the modulation efficiency usinga grating in the transition band with a semiconductor waveguide that hasstrong electro-absorption and/or electro-refraction is another potentialapplication of this invention. In analog applications, linearization ofthe R or T curve near the bias point will be an important designconsideration to increase the Spurious Free Dynamic range. In digitalapplications, apodization of the grating will be considered to reducethe sensitivity of the on/off ratio to the switching and bias voltages.

An Example of Optical Modulation at the Band Edge of Periodic Structureson LiNbO₃ Waveguides

The Mach-Zehnder LiNbO₃ modulator has been used for external modulationin many fiber optical applications. There is keen interest in anytechnique that will increase its modulation efficiency so that the fiberoptical communication systems can be operated with much lower drivingvoltage. The technique of optical modulation at the grating band edgemay offer such important improvements. It is demonstrated by simulationhere.

A typical x-cut LiNbO₃ channel waveguide phase modulator with electrodeconfiguration and Ti diffused channel is shown in FIG. 5. The change ofthe effective index of the TE₀₀ mode as a function of the voltageapplied to the electrodes is shown in FIG. 6. Although different designsof the electrode and the channel may give a different effective indexcurve, the performance of the electro-optical change of effective indexcan be illustrated in terms of the curves in FIG. 6 without any loss ofgenerality. The simulation is done for the 1.3 μm wavelength. For such awaveguide with a grating fabricated in polymers or in SiO₂ (index=1.5)on top, the C₀ as a function of the grating corrugation depth is shownin FIG. 7. Since the grating periodicity for Bragg reflection at the 1.5μm wavelength is approximately 3.5 μm, the corrugation depth that can beetched effectively by conventional methods without special etchingtechnique is less than 3.5 μm. Since the guided wave mode decaysexponentially in the low index cladding, the C₀ value saturates at largecorrugation depth. If a high index material such as titanium oxide isused as the grating material, larger C₀ can be obtained withoutsaturation. An alternative is to use reactive ion etch techniques toetch a grating directly into the LiNbO₃ waveguide.

FIG. 8 shows the equivalent V_(π) of a reflection band edge modulator asa function of grating length at C₀=5 mm⁻¹ for waveguide propagation lossat 0.1 and 0.3 dB/cm. FIG. 8 is an illustration of the modulationefficiency, measured in terms of the equivalent V_(π), that can beobtained for typical cases. Here, the equivalent V_(π) is defined asπ/(|2dR/dV|) for analog modulation. Larger C₀ and lower loss will yieldbetter performance. For digital modulation, the V_(mod) is the voltageswing from the “on” state to the “off” state. The digital V_(mod) isroughly three times the equivalent Vπ. Based on the electrodeconfiguration shown in FIG. 5, the capacitance per unit length of alumped element electrode can be calculated. The calculated bandwidth ofthe RC effect at L=5 and 10 mm are also shown in this figure. Smallpropagation loss does not reduce Vπ much for L less than 5 mm. For L<5mm, an increase of C₀ would be effective in reducing V_(π). On the otherhand, for L≧10 mm, the effect of propagation loss is pronounced. FIG. 9shows the V_(π) as a function of the RC limited bandwidth for thecommon-case grating band edge modulators in comparison with other LiNbO₃and polymer modulators. (S.-H. Lee et al., IEEE J. Quantum Electron.,vol. 36, no. 5, pp. 527-532, 2000; Y. Shi et al., Appl. Phys. Lett.,vol. 77, no. 1, pp. 1-3, 2000; W. K. Burns et al., J. LightwaveTechnol., vol. 17, no. 2, pp. 2551-2555, 1999; K. Noguchi et al., inTechnical digest of CLEO/Pacific Rim '99, vol. 4, (IEEE, Piscataway,N.J.), pp.1267-1268, 1999.) Even with C₀=5 mm⁻¹ at 3 GHz bandwidth, theV_(π) of the band edge modulator is lower than other comparablemodulators. A large reduction in V_(π) is achievable at lower bandwidth.If a large C₀ can be obtained (e.g., using the TiO₂ material or etchedgrating), the V_(π) can be even lower, and to the modulator can have alarger bandwidth. However, because of the bandwidth limitations, it isunlikely that the V_(π) of the grating band edge modulator can be betterthan the traveling wave modulators at 30 or 40 GHz bandwidth.

Optical Modulation at the Band Edge of Periodic Structures in OtherElectro-optic Channel waveguides

The band edge effect of periodic structures can also be applied tosemiconductor channel waveguides. In addition, besides the normalelectro-optic change of index far away from the absorption of thematerial, some semiconductor waveguide materials have Frantz-Keldysh orQuantum Confined Stark Effect near their absorption band edge or excitonabsorption. These materials may exhibit very strong changes inabsorption as a function of the applied electric field called theelectro-absorption effect and/or very large changes in refractive indexas a function of the applied electric field called theelectro-refraction effect. Using the band edge dispersion coupled withvary large electro-absorption and/or electro-refraction may yield muchmore effective modulation than either LiNbO₃ or polymer waveguides. Theobvious long term advantage of semiconductor modulator is its potentialfor integration with other optical components such as laser and/orintegration with electronic driver or detector circuits on the samechip.

A polymeric waveguide modulator is potentially attractive for manyoptical fiber applications. It has many potential advantages. Forexample, polymer material can be coated easily on other materials. Itcan be used to integrate electronic circuits with optical modulators.The difference between microwave and optical index of polymers is muchsmaller than LiNbO₃. Therefore the bandwidth limitation in travelingwave devices due to microwave and optical phase mismatch is muchsmaller.

Polymeric waveguides differ from LiNbO₃ waveguides in their materialproperties. They are made from low index materials. Different materialproperties are obtained by different synthesis and pulling processes. Itis necessary to consider the effect of both the TE and the TMpropagating modes, variations in electro-optical coefficients anddifferent propagation losses. The primary disadvantages of currentpolymeric waveguides are their large propagation loss and moderateelectro-optical coefficient. Typical propagation loss andelectro-optical coefficients are ˜1.5 dB/cm loss and 28 pm/V EOcoefficient for the TM mode, and ˜0.75 dB/cm loss and 9 pm/V EOcoefficient for the TE mode. Since the material properties are beingimproved continuously, simulation and demonstration of modulation at theband edge of periodic structures constitute an ongoing project.

Many applications of the invention are possible. The foregoing examplesare provided for illustrative purposes. Potentially, many fiber opticallinks using external modulation of the loser power may use this deviceinstead of the existing devices. Thus the potential number of uses isvery large, including telecommunication, CATV, wireless communication,RF photonic links, phased array, antenna remoting, sensor, etc.

While various embodiments of the present invention have been shown anddescribed, it should be understood that other modifications,substitutions and alternatives are apparent to one of ordinary skill inthe art. Such modifications, substitutions and alternatives can be madewithout departing from the spirit and scope of the invention, whichshould be determined from the appended claims.

Various features of the invention are set forth in the appended claims.

1. A method for optical modulation, the method comprising steps of:employing an optical modulator including a waveguide and a grating uponthe waveguide, said optical modulator having its band edge regionmatched to an optical wavelength of interest for modulation; andcontrolling one of the transmission and reflection of an optical wavefrom said optical modulator near the band edge region.
 2. The methodaccording to claim 1, wherein said step of controlling comprisesmonitoring and controlling a wavelength of incident radiation used tostimulate the transmission and reflection from said optical modulator.3. The method according to claim 1, wherein said step of controllingcomprises changing a material refractive index of the optical modulator.4. The method according to claim 1, wherein said step of controllingcomprises changing a material absorption index of the optical modulator.5. A method for optical modulation using a periodic optical structurehaving a waveguide and a grating structure with broad pass bands andnarrow transition bands, the method comprising steps of: exposing theperiodic optical structure to an incident laser wavelength in the middleof one of the transition bands or at the beginning of one of thetransition bands; controlling modulation of the incident laser at agiven wavelength by applying a modulation voltage to the periodicoptical structure.
 6. The method for optical modulation according toclaim 5, wherein the periodic optical structure comprises aone-dimensional optical grating coupled to a parallel optical waveguide.7. The method according to claim 6, wherein the optical grating has acoupling coefficient and length to create wide pass bands with rapidtransitions from pass to stop bands as a function of effective index ofthe waveguide.
 8. The method according to claim 5, wherein the waveguidecomprises a LiNbO₃ waveguide and the grating is formed upon a SiO_(x) orpolymer buffer layer.
 9. A method for designing a periodic opticalstructure having broad pass bands with narrow transition bands, theoptical structure being suited for optical modulation at a band edge ofthe narrow transition bands, the optical structure including a waveguideand an optical grating, the method comprising steps of choosing a highcoupling coefficient for the waveguide material; choosing a bias voltageapplied to the optical waveguide and a grating periodicity so that itsBragg wavelength is mismatched with the laser wavelength, and selectinga grating length to enhance modulation efficiency.
 10. The methodaccording to claim 9, wherein said step of selecting comprisesoptimizing the grating length to achieve a high on/off modulation ratiowith a smallest change of effective index by the signal voltage.
 11. Amethod, comprising: providing light to an optical modulator having afirst transition band between a pass band and a stop band; controllingtransmission of said light in or near the first transition band.
 12. Themethod of claim 11, wherein said modulator includes a periodic opticalstructure coupled to an optical waveguide.
 13. The method of claim 11,wherein said controlling includes controlling a wavelength of saidlight.
 14. The method of claim 11, wherein said controlling includeschanging a refractive index of said modulator.
 15. The method of claim11, wherein said controlling includes changing an absorption of saidmodulator.
 16. A method, comprising: providing light to an opticalmodulator having a first transition band between a pass band and a stopband; controlling reflection of said light in or near the firsttransition band.
 17. The method of claim 16, wherein said modulatorincludes a periodic optical structure coupled to an optical waveguide.18. The method of claim 16, wherein said controlling includescontrolling a wavelength of said light.
 19. The method of claim 16,wherein said controlling includes changing a refractive index of saidmodulator.
 20. The method of claim 16, wherein said controlling includeschanging an absorption of said modulator.
 21. A method, comprising:providing light having a first wavelength to an apparatus that includesa periodic optical structure and an optical waveguide, wherein saidapparatus has a first transition band between a pass band and a stopband, and wherein said first wavelength is in the beginning or themiddle of said first transition band; applying a voltage to theapparatus in order to modulate said light within said first wavelength.22. The method of claim 21, wherein said applied voltage changes arefractive index of said apparatus.
 23. The method of claim 21, whereinsaid applied voltage changes an absorption of said apparatus.
 24. Themethod of claim 21, wherein said periodic optical structure is agrating, and wherein said light is incident laser radiation.
 25. Anoptical modulation system comprising: an optical waveguide; a periodicoptical structure coupled to said optical waveguide to provide anoptical modulator having a first transition band for incident light, thefirst transition band being between a pass band and a stop band; saidoptical modulator being responsive to voltage for controllingtransmission of the incident light for said optical modulator in or nearsaid first transition band.
 26. The optical modulation system of claim25, wherein said voltage controls a wavelength of said incident light.27. The optical modulation system of claim 25, wherein said voltagechanges a refractive index of said optical modulator.
 28. The opticalmodulation system of claim 25, wherein said voltage changes anabsorption of said optical modulator.
 29. The optical modulation systemof claim 25, further comprising: a source for said voltage.
 30. Theoptical modulation system of claim 25, wherein said periodic opticalstructure comprises a grating.